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Journal articles on the topic 'Mathematical modelling/biology'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Vasieva, Olga, Manan'Iarivo Rasolonjanahary, and Bakhtier Vasiev. "Mathematical modelling in developmental biology." REPRODUCTION 145, no. 6 (2013): R175—R184. http://dx.doi.org/10.1530/rep-12-0081.

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In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies

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2

Tomlin, Claire J., and Jeffrey D. Axelrod. "Biology by numbers: mathematical modelling in developmental biology." Nature Reviews Genetics 8, no. 5 (2007): 331–40. http://dx.doi.org/10.1038/nrg2098.

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3

Jäger, Willi. "Mathematical Modelling in Chemistry and Biology." Interdisciplinary Science Reviews 11, no. 2 (1986): 181–88. http://dx.doi.org/10.1179/isr.1986.11.2.181.

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4

Chaplain, M. A. J. "Multiscale mathematical modelling in biology and medicine." IMA Journal of Applied Mathematics 76, no. 3 (2011): 371–88. http://dx.doi.org/10.1093/imamat/hxr025.

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5

Lei, Jinzhi. "Viewpoints on modelling: Comments on "Achilles and the tortoise: Some caveats to mathematical modelling in biology"." Mathematics in Applied Sciences and Engineering 1, no. 1 (2020): 85–90. http://dx.doi.org/10.5206/mase/10267.

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Mathematical modelling has been proven to be useful in understanding some problems from biological science, provided that it is used properly. However, it has also attracted some criticisms as partially presented in a recent opinion article \cite{Gilbert2018} from biological community. This note intends to clarify some confusion and misunderstanding in regard to mathematically modelling by commenting on those critiques raised in \cite{Gilbert2018}, with a hope of initiating some further discussion so that both applied mathematicians and biologist can better use mathematical modelling and bette

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6

Middleton, A., M. Owen, M. Bennett, and J. King. "Mathematical modelling of gibberellinsignalling." Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology 150, no. 3 (2008): S46. http://dx.doi.org/10.1016/j.cbpa.2008.04.023.

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7

Butler, George, Jonathan Rudge, and Philip R. Dash. "Mathematical modelling of cell migration." Essays in Biochemistry 63, no. 5 (2019): 631–37. http://dx.doi.org/10.1042/ebc20190020.

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Abstract The complexity of biological systems creates challenges for fully understanding their behaviour. This is particularly true for cell migration which requires the co-ordinated activity of hundreds of individual components within cells. Mathematical modelling can help understand these complex systems by breaking the system into discrete steps which can then be interrogated in silico. In this review, we highlight scenarios in cell migration where mathematical modelling can be applied and discuss what types of modelling are most suited. Almost any aspect of cell migration is amenable to ma

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8

Divya, B., and K. Kavitha. "A REVIEW ON MATHEMATICAL MODELLING IN BIOLOGY AND MEDICINE." Advances in Mathematics: Scientific Journal 9, no. 8 (2020): 5869–79. http://dx.doi.org/10.37418/amsj.9.8.54.

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9

MacArthur, B. D., C. P. Please, M. Taylor, and R. O. C. Oreffo. "Mathematical modelling of skeletal repair." Biochemical and Biophysical Research Communications 313, no. 4 (2004): 825–33. http://dx.doi.org/10.1016/j.bbrc.2003.11.171.

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10

Shone, John. "Working at the biology/mathematics interface: mathematical modelling and sixth form biology." International Journal of Mathematical Education in Science and Technology 19, no. 4 (1988): 501–9. http://dx.doi.org/10.1080/0020739880190402.

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11

Friedman, Avner. "Free boundary problems in biology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2050 (2015): 20140368. http://dx.doi.org/10.1098/rsta.2014.0368.

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In this paper, I review several free boundary problems that arise in the mathematical modelling of biological processes. The biological topics are quite diverse: cancer, wound healing, biofilms, granulomas and atherosclerosis. For each of these topics, I describe the biological background and the mathematical model, and then proceed to state mathematical results, including existence and uniqueness theorems, stability and asymptotic limits, and the behaviour of the free boundary. I also suggest, for each of the topics, open mathematical problems.

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12

Lampl, Michelle. "Perspectives on modelling human growth: Mathematical models and growth biology." Annals of Human Biology 39, no. 5 (2012): 342–51. http://dx.doi.org/10.3109/03014460.2012.704072.

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13

Eftimie, Raluca. "The quest for a new modelling framework in mathematical biology." Physics of Life Reviews 12 (March 2015): 72–73. http://dx.doi.org/10.1016/j.plrev.2015.01.012.

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14

Alfonso, J. C. L., K. Talkenberger, M. Seifert, et al. "The biology and mathematical modelling of glioma invasion: a review." Journal of The Royal Society Interface 14, no. 136 (2017): 20170490. http://dx.doi.org/10.1098/rsif.2017.0490.

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Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential me

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15

Maini, P. K. "Essential Mathematical Biology." Mathematical Medicine and Biology 20, no. 2 (2003): 225–26. http://dx.doi.org/10.1093/imammb/20.2.225.

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16

Geris, L., J. Vander Sloten, and H. Van Oosterwyck. "In silico biology of bone modelling and remodelling: regeneration." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1895 (2009): 2031–53. http://dx.doi.org/10.1098/rsta.2008.0293.

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Bone regeneration is the process whereby bone is able to (scarlessly) repair itself from trauma, such as fractures or implant placement. Despite extensive experimental research, many of the mechanisms involved still remain to be elucidated. Over the last decade, many mathematical models have been established to investigate the regeneration process in silico . The first models considered only the influence of the mechanical environment as a regulator of the healing process. These models were followed by the development of bioregulatory models where mechanics was neglected and regeneration was r

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17

Lewis, Rohan M., Jane K. Cleal, and Bram G. Sengers. "Placental perfusion and mathematical modelling." Placenta 93 (April 2020): 43–48. http://dx.doi.org/10.1016/j.placenta.2020.02.015.

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18

Huber, Heinrich J., Heiko Duessmann, Jakub Wenus, Seán M. Kilbride, and Jochen H. M. Prehn. "Mathematical modelling of the mitochondrial apoptosis pathway." Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1813, no. 4 (2011): 608–15. http://dx.doi.org/10.1016/j.bbamcr.2010.10.004.

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19

Alexander, R. McN. "Modelling approaches in biomechanics." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1437 (2003): 1429–35. http://dx.doi.org/10.1098/rstb.2003.1336.

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Conceptual, physical and mathematical models have all proved useful in biomechanics. Conceptual models, which have been used only occasionally, clarify a point without having to be constructed physically or analysed mathematically. Some physical models are designed to demonstrate a proposed mechanism, for example the folding mechanisms of insect wings. Others have been used to check the conclusions of mathematical modelling. However, others facilitate observations that would be difficult to make on real organisms, for example on the flow of air around the wings of small insects. Mathematical m

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20

Ehrhardt, Matthias, Lucas Jódar Sánchez, and Rafael Jacinto Villanueva Micó. "Numerical methods and mathematical modelling in biology, medicine and social sciences." International Journal of Computer Mathematics 91, no. 2 (2014): 176–78. http://dx.doi.org/10.1080/00207160.2014.896653.

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21

Brunetti, Mia, Michael C. Mackey, and Morgan Craig. "Understanding Normal and Pathological Hematopoietic Stem Cell Biology Using Mathematical Modelling." Current Stem Cell Reports 7, no. 3 (2021): 109–20. http://dx.doi.org/10.1007/s40778-021-00191-9.

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22

Vera, Julio, Christopher Lischer, Momchil Nenov, Svetoslav Nikolov, Xin Lai, and Martin Eberhardt. "Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic." International Journal of Molecular Sciences 22, no. 2 (2021): 547. http://dx.doi.org/10.3390/ijms22020547.

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In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today’s level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than a

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23

Vera, Julio, Christopher Lischer, Momchil Nenov, Svetoslav Nikolov, Xin Lai, and Martin Eberhardt. "Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic." International Journal of Molecular Sciences 22, no. 2 (2021): 547. http://dx.doi.org/10.3390/ijms22020547.

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In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today’s level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than a

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24

McDonald, Andrew G., Keith F. Tipton, and Gavin P. Davey. "Mathematical modelling of metabolism: Summing up." Biochemist 31, no. 3 (2009): 24–27. http://dx.doi.org/10.1042/bio03103024.

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Biochemistry is as much a quantitative subject as qualitative. Initial observations of single- or multicellular organisms have given rise to our discipline, which is the discovery and characterization of the chemistry of all living things. We have moved from Lavoisier's seminal observation of respiration as a form of combustion, to a much more detailed knowledge of the associated biochemistry.

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25

Shelah, Saharon, and Lutz Strüngmann. "Infinite combinatorics in mathematical biology." Biosystems 204 (June 2021): 104392. http://dx.doi.org/10.1016/j.biosystems.2021.104392.

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26

Priori, Luca, and Paolo Ubezio. "Mathematical modelling and computer simulation of cell synchrony." Methods in Cell Science 18, no. 2 (1996): 83–91. http://dx.doi.org/10.1007/bf00122158.

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27

Ribba, Benjamin, Philippe Tracqui, Jean-Laurent Boix, Jean-Pierre Boissel, and S. Randall Thomas. "Q x DB: a generic database to support mathematical modelling in biology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1843 (2006): 1517–32. http://dx.doi.org/10.1098/rsta.2006.1784.

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Q x DB (quantitative x -modelling database) is a web-based generic database package designed especially to house quantitative and structural information. Its development was motivated by the need for centralized access to such results for development of mathematical models, but its usefulness extends to the general research community of both modellers and experimentalists. Written in PHP (Hyper Preprocessor) and MySQL , the database is easily adapted to new fields of research and ported to Apache-based web servers. Unlike most existing databases, experimental and observational results curated

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28

Torres, Néstor V. "Introducing Systems Biology to Bioscience Students through Mathematical Modelling. A Practical Module." Bioscience Education 21, no. 1 (2013): 54–63. http://dx.doi.org/10.11120/beej.2013.00012.

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29

Auger, Pierre, and Jean-Christophe Poggiale. "Mathematical modelling is a necessary step in biology and in environmental sciences." Comptes Rendus Geoscience 338, no. 4 (2006): 223–24. http://dx.doi.org/10.1016/j.crte.2006.01.004.

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30

Prpic, Nikola-Michael, and Nico Posnien. "Size and shape—integration of morphometrics, mathematical modelling, developmental and evolutionary biology." Development Genes and Evolution 226, no. 3 (2016): 109–12. http://dx.doi.org/10.1007/s00427-016-0536-5.

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31

Wearing, H. "Mathematical Modelling of Juxtacrine Patterning." Bulletin of Mathematical Biology 62, no. 2 (2000): 293–320. http://dx.doi.org/10.1006/bulm.1999.0152.

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32

Smallbone, Kieran, Robert A. Gatenby, and Philip K. Maini. "Mathematical modelling of tumour acidity." Journal of Theoretical Biology 255, no. 1 (2008): 106–12. http://dx.doi.org/10.1016/j.jtbi.2008.08.002.

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33

Liebal, Ulf W., Thomas Millat, Imke G. De Jong, Oscar P. Kuipers, Uwe Völker, and Olaf Wolkenhauer. "How mathematical modelling elucidates signalling in Bacillus subtilis." Molecular Microbiology 77, no. 5 (2010): 1083–95. http://dx.doi.org/10.1111/j.1365-2958.2010.07283.x.

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34

Meades, G., N. K. Thalji, M. de Queiroz, X. Cai, and G. L. Waldrop. "Mathematical modelling of negative feedback regulation by carboxyltransferase." IET Systems Biology 5, no. 3 (2011): 220–28. http://dx.doi.org/10.1049/iet-syb.2010.0071.

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35

Rangamani, Padmini, and Ravi Iyengar. "Modelling cellular signalling systems." Essays in Biochemistry 45 (September 30, 2008): 83–94. http://dx.doi.org/10.1042/bse0450083.

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Cell signalling pathways and networks are complex and often non-linear. Signalling pathways can be represented as systems of biochemical reactions that can be modelled using differential equations. Computational modelling of cell signalling pathways is emerging as a tool that facilitates mechanistic understanding of complex biological systems. Mathematical models are also used to generate predictions that may be tested experimentally. In the present chapter, the various steps involved in building models of cell signalling pathways are discussed. Depending on the nature of the process being mod

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36

Cho, K. H., and O. Wolkenhauer. "Analysis and modelling of signal transduction pathways in systems biology." Biochemical Society Transactions 31, no. 6 (2003): 1503–9. http://dx.doi.org/10.1042/bst0311503.

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There is general agreement that a systems approach is needed for a better understanding of causal and functional relationships that generate the dynamics of biological networks and pathways. These observations have been the basis for efforts to get the engineering and physical sciences involved in life sciences. The emergence of systems biology as a new area of research is evidence for these developments. Dynamic modelling and simulation of signal transduction pathways is an important theme in systems biology and is getting growing attention from researchers with an interest in the analysis of

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37

Ali Lashari, Abid, and Faiz Ahmad. "False mathematical reasoning in biology." Journal of Theoretical Biology 307 (August 2012): 211. http://dx.doi.org/10.1016/j.jtbi.2012.05.006.

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38

Westerhoff, Hans V. "Mathematical and theoretical biology for systems biology, and then ... vice versa." Journal of Mathematical Biology 54, no. 1 (2006): 147–50. http://dx.doi.org/10.1007/s00285-006-0043-9.

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39

Varner, J. D. "Systems biology and the mathematical modelling of antibody-directed enzyme prodrug therapy (ADEPT)." IEE Proceedings - Systems Biology 152, no. 4 (2005): 291. http://dx.doi.org/10.1049/ip-syb:20050047.

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40

Burrows, M. T. "Modelling biological populations in space and time: Cambridge studies in mathematical biology: 11." Journal of Experimental Marine Biology and Ecology 168, no. 1 (1993): 139–40. http://dx.doi.org/10.1016/0022-0981(93)90120-d.

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41

MUKHERJEE, SHIBAJI, and SUSHMITA MITRA. "HIDDEN MARKOV MODELS, GRAMMARS, AND BIOLOGY: A TUTORIAL." Journal of Bioinformatics and Computational Biology 03, no. 02 (2005): 491–526. http://dx.doi.org/10.1142/s0219720005001077.

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Biological sequences and structures have been modelled using various machine learning techniques and abstract mathematical concepts. This article surveys methods using Hidden Markov Model and functional grammars for this purpose. We provide a formal introduction to Hidden Markov Model and grammars, stressing on a comprehensive mathematical description of the methods and their natural continuity. The basic algorithms and their application to analyzing biological sequences and modelling structures of bio-molecules like proteins and nucleic acids are discussed. A comparison of the different appro

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42

Axenie, Cristian, Roman Bauer, and María Rodríguez Martínez. "The Multiple Dimensions of Networks in Cancer: A Perspective." Symmetry 13, no. 9 (2021): 1559. http://dx.doi.org/10.3390/sym13091559.

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This perspective article gathers the latest developments in mathematical and computational oncology tools that exploit network approaches for the mathematical modelling, analysis, and simulation of cancer development and therapy design. It instigates the community to explore new paths and synergies under the umbrella of the Special Issue “Networks in Cancer: From Symmetry Breaking to Targeted Therapy”. The focus of the perspective is to demonstrate how networks can model the physics, analyse the interactions, and predict the evolution of the multiple processes behind tumour-host encounters acr

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43

Rittscher, Jens, Andrew Blake, Anthony Hoogs, and Gees Stein. "Mathematical modelling of animate and intentional motion." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1431 (2003): 475–90. http://dx.doi.org/10.1098/rstb.2002.1259.

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Our aim is to enable a machine to observe and interpret the behaviour of others. Mathematical models are employed to describe certain biological motions. The main challenge is to design models that are both tractable and meaningful. In the first part we will describe how computer vision techniques, in particular visual tracking, can be applied to recognize a small vocabulary of human actions in a constrained scenario. Mainly the problems of viewpoint and scale invariance need to be overcome to formalize a general framework. Hence the second part of the article is devoted to the question whethe

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44

Owen, Markus R., and Jonathan A. Sherratt. "Mathematical modelling of juxtacrine cell signalling." Mathematical Biosciences 153, no. 2 (1998): 125–50. http://dx.doi.org/10.1016/s0025-5564(98)10034-2.

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45

Lemon, Greg, Daniel Howard, Matthew J. Tomlinson, et al. "Mathematical modelling of tissue-engineered angiogenesis." Mathematical Biosciences 221, no. 2 (2009): 101–20. http://dx.doi.org/10.1016/j.mbs.2009.07.003.

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46

Baigent, Stephen, Robert Unwin, and Chee Chit Yeng. "Mathematical Modelling of Profiled Haemodialysis: A Simplified Approach." Journal of Theoretical Medicine 3, no. 2 (2001): 143–60. http://dx.doi.org/10.1080/10273660108833070.

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For many renal patients with severe loss of kidney function dialysis treatment is the only means of preventing excessive fluid gain and the accumulation of toxic chemicals in the blood. Typically, haemodialysis patients will dialyse three times a week, with each session lasting 4-6 hours. During each session, 2-3 litres of fluid is removed along with catabolic end-products, and osmotically active solutes. In a significant number of patients, the rapid removal of water and osmotically active sodium chloride can lead to hypotension or overhydration and swelling of brain cells. Profiled haemodial

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47

Marshall, James A. R., Andreagiovanni Reina, and Thomas Bose. "Multiscale Modelling Tool: Mathematical modelling of collective behaviour without the maths." PLOS ONE 14, no. 9 (2019): e0222906. http://dx.doi.org/10.1371/journal.pone.0222906.

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48

Alt, Wolfgang. "ESMTB – European Society for Mathematical and Theoretical Biology." Journal of Mathematical Biology 53, no. 3 (2006): 337–39. http://dx.doi.org/10.1007/s00285-006-0030-1.

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49

Deutsch, Andreas. "ESMTB-European Society for Mathematical and Theoretical Biology." Journal of Mathematical Biology 53, no. 5 (2006): 887–88. http://dx.doi.org/10.1007/s00285-006-0041-y.

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50

Diekmann, Odo, Klaus Dietz, Thomas Hillen, and Horst Thieme. "Karl-Peter Hadeler: His legacy in mathematical biology." Journal of Mathematical Biology 77, no. 6-7 (2018): 1623–27. http://dx.doi.org/10.1007/s00285-018-1259-1.

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